Question

A piece of chalk of diameter $d$ is subjected to an axial load $P$ and a torque $T$. Assume that the chalk remains linearly elastic up to the ultimate strength $\sigma_{\mathrm{u}}$. The axial load is $P=\sigma_{\mathrm{u}} \pi d^2 / 12$. Determine the magnitude of the torque $T$ that will cause brittle fracture.

   A piece of chalk of diameter $d$ is subjected to an axial load $P$ and a torque $T$. Assume that the chalk remains linearly elastic up to the ultimate strength $\sigma_{\mathrm{u}}$. The axial load is $P=\sigma_{\mathrm{u}} \pi d^2 / 12$. Determine the magnitude of the torque $T$ that will cause brittle fracture.

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Advanced Mechanics of Materials

Advanced Mechanics of Materials

Arthur P. Boresi,… 6th Edition

Chapter 15, Problem 2

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Step 1

The shear stress due to the applied torque can be expressed as: \[ \tau = \frac{T \cdot r}{J} \] where \( r \) is the radius of the chalk, and \( J \) is the polar moment of inertia for a circular cross-section, given by: \[ J = \frac{\pi d^4}{32} \] Show more…

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A piece of chalk of diameter $d$ is subjected to an axial load $P$ and a torque $T$. Assume that the chalk remains linearly elastic up to the ultimate strength $\sigma_{\mathrm{u}}$. The axial load is $P=\sigma_{\mathrm{u}} \pi d^2 / 12$. Determine the magnitude of the torque $T$ that will cause brittle fracture.

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